Example
Outline of building and approach wind characteristics
Building height H = 200 m
Building width B = 40 m
Building depth D = 40 m
Building natural frequency f_{1x }= 0.2 Hz, f_{1y }= 0.2 Hz, f_{1z} = 0.35 Hz
Average radius of gyration g = 18 m
Linear mode shape in all three directions
Damping ratio z= 0.02 (Composite Structural System)
Drag force coefficient C_{D }= 1.3
Building bulk density is 250 kg
/m^{3}
Air density r = 1.25 kg /m^{3}
According to ASCE798, this site is defined as Exposure A from all
directions, with a = 1/3.0 (Table 64, ASCE 798)
Basic wind speed at reference height of 10 m in terms of 3second
gust, U_{10} = 63 m/s (Fig. 61b, ASCE 798)
Note: The influences of wind direction, topography, shielding,
importance factor, and return period are ignored in the discussion herein.
STEP 1. Computation of reduced frequency _{}
The first step is to calculate the
reduced frequency in terms of the mean wind speed at the building’s full height
in Exposure Category A. This requires several conversions: (A) convert the wind
speed at 10 m height in from a 3 second gust in open terrain to a wind speed
with averaging time of 1 hour in Exposure A; (B) convert to fullheight of the
structure. Two scenarios are considered, the survivability design with a
50year event for determination of base moments, and the serviceability design
with a 10year event for determination of RMS acceleration levels.
Survivability design
(onehour averaging time, 50year return period) 

Wind
speed at 10 m height in terms of 3second gust in open terrain = 63 m/s 

A)
Conversion to wind speed in terms of 1hour mean in Exposure A = 63 ´ 0.30* = 18.9 m/s 

B)
Conversion to wind speed at 200 m height in terms of 1hour mean in Exposure
A = _{} = 18.9 ´ (200/10)^{ 1/3} = 51.30 m/s 

_{} = 0.156 
_{} = 0.156 
_{} = 0.273 
Serviceability design
(onehour averaging time, 10year return period) 

Conversion
to 3second gust at 10 m height in open terrain for 10 year return period =
63 ´ 0.74** = 46.62 m/s 

A)
Conversion to 1hour mean wind speed in Exposure A = 46.62 ´ 0.30* = 13.99 m/s 

B)
Conversion to wind speed at 200 m height in terms of 1hour mean in Exposure
A = _{} = 13.99 ´ (200/10) ^{1/3} = 37.96 m/s 

_{}= 0.211 
_{}= 0.211 
_{}= 0.369 
*Conversion factor, _{}, taken from Table 64 (ASCE 798) **Conversion
factor shown in Table C63 (ASCE 798) 
STEP 2. Access database for RMS moment coefficients and spectral
values
Using the Aerodynamic
Loads Database for the case shown here, the values of the nondimensionalized
power spectrum and RMS coefficient can be identified. Note that these values
have been rounded to three decimal places in this example. The accompanying
snap shot illustrates this process for the alongwind survivability case.

_{} 
_{} 
_{} 

50year 
10year 
50year 
10year 

Alongwind 
0.109 
0.156 
0.211 
0.048 
0.040 
Acrosswind 
0.133 
0.156 
0.211 
0.192 
0.073 
Torsional 
0.044 
0.273 
0.369 
0.059 
0.040 
3. Look for RMS moment coefficients and spectral values from the database
STEP 3. Compute base moments and acceleration response
Using the values provided by the database, the background and
resonant components of the base bending moment and base torque can be computed
by Equations 11 and 12, as given in the procedure section of this
website. The expression for the resonant peak factor is provided in the
procedure, while the background peak factor can be assumed to be 3.4, in
accordance with ASCE 798.
While the mean base moment for the acrosswind and torsional
response is assumed zero, the alongwind mean base moment can be calculated by
integrating the mean loads over the height:
(13)
where the mean wind load per unit height is given by .
The peak base moment can then be determined in accordance with the
combination rule (Eq. 7) in the procedure.
The values for the survivability design
according the database are provided alongside the alongwind peak base moment
determined from ASCE 798.

Base moments
(10^{6} kNm) 

_{} 
_{} 
_{} 
_{} 

Alongwind
by ASCE798 
3.2790* 
 
 
3.3117** 
Alongwind 
1.2831 
0.9754 
1.4915 
3.0651 
Acrosswind 
0.0000 
1.1902 
3.6396 
3.8293 
Torsional 
0.0000 
0.0788 
0.1386 
0.1594 
*Mean base moment, in 3second averaging time. All other results in terms of 1hour averaging time. , where the gust effect factor, G=1.01, as determined by Eq. 66 (ASCE 798). **Determined by net effect of pressures prescribed by Eq. 617 on
windward and leeward faces, integrated over full height of structure. 
Serviceability
Design (10 year wind)
In the case of serviceability
design for occupant comfort, RMS accelerations for a 10year event become
critical. Equation 8 in the procedure provided
can be used to obtain peak accelerations, whose division by the resonant peak
factor yields the RMS accelerations provided below. This requires the
determination of the resonant component of the equivalent static wind loads
given by Equations 5 & 6, in addition to the resonant base moments. In the
case of the torsional component, the mass moment of inertia per unit height,
I(z), is defined as m(z)g^{2} where g is the radius of gyration.
The angular
accelerations due to torsion may be separated into the resultant alongwind and
acrosswind components at the corner of the structure, as shown by the
accompanying figure. These lateral accelerations induced by torsion can be
combined with those generated by sway motion to obtain the total lateral
accelerations at the corner by the SRSS combination rule. Once again, ASCE 798
calculations for the alongwind accelerations are provided for comparison.

RMS Accelerations at roof 

Alongwind
by ASCE 798 
3.84 millig 

Alongwind 
3.76 millig 

Acrosswind 
6.20 millig 

Lateral Accelerations at Corner Induced by Torsion 
1.20´10^{3} rad/s^{2} 
Alongwind component: 2.50 millig 
Acrosswind component: 2.50 millig 

Total Lateral Accelerations at Corner 
Alongwind component: 4.52 millig Acrosswind component: 6.69 millig 
To illustrate the contributions of the
background and resonant components in the various directions to the overall
wind forces, the distribution of these wind force components along the building
height are given in the plots and table below. While expressions for the
resonant component of the equivalent static wind loads is provided by Equations
5 & 6 in the procedure,
the methodology for the background component of these loads can be determined
by expressions provided in Zhou and Kareem 2001.
In this description, the wind loads are defined as point loads at each floor of
the structure, assuming the floortofloor height to be 4 m.
Table
1: Equivalent static wind loads
Height (m) 
A 
B 
C 
D 
E 
F 
G 
4 
25.21 
19.165 
8.686 
23.385 
21.198 
193.406 
108.704 
8 
40.018 
30.422 
17.372 
37.121 
42.395 
307.013 
217.408 
12 
52.439 
39.864 
26.059 
48.642 
63.593 
402.301 
326.113 
16 
63.525 
48.292 
34.745 
58.925 
84.79 
487.353 
434.817 
20 
73.715 
56.038 
43.431 
68.377 
105.988 
565.523 
543.521 
24 
83.242 
63.281 
52.117 
77.214 
127.186 
638.614 
652.225 
28 
92.251 
70.13 
60.804 
85.571 
148.383 
707.733 
760.93 
32 
100.84 
76.659 
69.49 
93.538 
169.581 
773.625 
869.634 
36 
109.078 
82.921 
78.176 
101.179 
190.778 
836.82 
978.338 
40 
117.015 
88.955 
86.862 
108.542 
211.976 
897.712 
1087.042 
44 
124.691 
94.791 
95.549 
115.662 
233.173 
956.604 
1195.747 
48 
132.138 
100.452 
104.235 
122.57 
254.371 
1013.736 
1304.451 
52 
139.381 
105.958 
112.921 
129.288 
275.569 
1069.3 
1413.155 
56 
146.44 
111.324 
121.607 
135.836 
296.766 
1123.456 
1521.859 
60 
153.333 
116.564 
130.293 
142.23 
317.964 
1176.336 
1630.564 
64 
160.074 
121.689 
138.98 
148.483 
339.161 
1228.053 
1739.268 
68 
166.676 
126.708 
147.666 
154.607 
360.359 
1278.704 
1847.972 
72 
173.15 
131.629 
156.352 
160.612 
381.557 
1328.37 
1956.676 
76 
179.505 
136.46 
165.038 
166.507 
402.754 
1377.124 
2065.38 
80 
185.749 
141.207 
173.725 
172.299 
423.952 
1425.03 
2174.085 
84 
191.89 
145.876 
182.411 
177.996 
445.149 
1472.143 
2282.789 
88 
197.935 
150.471 
191.097 
183.602 
466.347 
1518.515 
2391.493 
92 
203.888 
154.997 
199.783 
189.125 
487.545 
1564.189 
2500.197 
96 
209.756 
159.458 
208.47 
194.568 
508.742 
1609.205 
2608.902 
100 
215.543 
163.857 
217.156 
199.935 
529.94 
1653.601 
2717.606 
104 
221.253 
168.198 
225.842 
205.232 
551.137 
1697.408 
2826.31 
108 
226.89 
172.483 
234.528 
210.461 
572.335 
1740.657 
2935.014 
112 
232.459 
176.716 
243.214 
215.626 
593.533 
1783.375 
3043.719 
116 
237.961 
180.899 
251.901 
220.73 
614.73 
1825.587 
3152.423 
120 
243.4 
185.034 
260.587 
225.776 
635.928 
1867.317 
3261.127 
124 
248.78 
189.124 
269.273 
230.765 
657.125 
1908.586 
3369.831 
128 
254.101 
193.169 
277.959 
235.702 
678.323 
1949.413 
3478.535 
132 
259.368 
197.173 
286.646 
240.587 
699.52 
1989.817 
3587.24 
136 
264.582 
201.136 
295.332 
245.423 
720.718 
2029.815 
3695.944 
140 
269.744 
205.061 
304.018 
250.212 
741.916 
2069.423 
3804.648 
144 
274.858 
208.949 
312.704 
254.956 
763.113 
2108.655 
3913.352 
148 
279.925 
212.8 
321.391 
259.655 
784.311 
2147.526 
4022.057 
152 
284.946 
216.617 
330.077 
264.313 
805.508 
2186.048 
4130.761 
156 
289.923 
220.401 
338.763 
268.93 
826.706 
2224.233 
4239.465 
160 
294.858 
224.153 
347.449 
273.508 
847.904 
2262.094 
4348.169 
164 
299.753 
227.873 
356.135 
278.047 
869.101 
2299.64 
4456.874 
168 
304.607 
231.564 
364.822 
282.55 
890.299 
2336.882 
4565.578 
172 
309.423 
235.225 
373.508 
287.018 
911.496 
2373.83 
4674.282 
176 
314.202 
238.858 
382.194 
291.45 
932.694 
2410.492 
4782.986 
180 
318.945 
242.463 
390.88 
295.85 
953.892 
2446.878 
4891.691 
184 
323.652 
246.042 
399.567 
300.217 
975.089 
2482.995 
5000.395 
188 
328.326 
249.595 
408.253 
304.552 
996.287 
2518.851 
5109.099 
192 
332.967 
253.123 
416.939 
308.857 
1017.484 
2554.454 
5217.803 
196 
337.576 
256.627 
425.625 
313.132 
1038.682 
2589.811 
5326.507 
200 
342.153 
260.106 
434.312 
317.378 
1059.879 
2624.927 
5435.212 